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Encyclopedia > Time in physics

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(Tagged November 2005)

In physics, the treatment of time is a central issue. It has been treated as a question of geometry. (See: philosophy of physics.) One can measure time and treat it as a geometrical dimension, such as length, and perform mathematical operations on it. It is a Scalar quantity and, like length, mass, and charge, is usually listed in most physics books as a fundamental quantity. Time can be combined mathematically with other fundamental quantities to derive other concepts such as motion, energy and fields. Time is largely defined by its measurement in physics. Physicists measure and use theories to predict measurements of time. What exactly time "is" and how it works is still largely undefined, except in relation to the other fundamental quantities. A black hole concept drawing by NASA. Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... A watch Attempting to understand time has long been a prime occupation for philosophers, scientists and artists. ... Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ... Philosophy of physics is the study of the fundamental, philosophical questions underlying modern physics, the study of matter and energy and how it interacts. ... Measure can mean: To perform a measurement. ... The term scalar is used in mathematics, physics, and computing basically for quantities that are characterized by a single numeric value and/or do not involve the concept of direction. ... In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... Charge is a word with many different meanings. ... In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, and weight, and units measure them. ... In Guy Debords words: ONE OF THE BASIC situationist practices is the dérive [literally: “drifting”], a technique of rapid passage through varied ambiances. ... In physics, motion means a change in the position of a body with respect to time, as measured by a particular observer in a particular frame of reference. ... In physics, a field is an assignment of a quantity to every point in space (or more generally, spacetime). ... For alternative meanings see definition (disambiguation) A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between a term and that terms meaning. ... Theory has a number of distinct meanings in different fields of knowledge, depending on the context and their methodologies. ...


Both Newton and Galileo and most people up until the 20th Century thought that time was the same for everyone everywhere. Our modern conception of time is based on Einstein's theory of relativity, in which rates of time run differently everywhere, and space and time are merged into spacetime. There is also a theoretical smallest time, the Planck time. Physicists, based on Einstein's general relativity as well as the redshift of the light from receeding distant galaxies, believe the entire Universe and therefore time itself began about thirteen billion years ago in the big bang. Whether it will ever come to an end is an open question. Sir Isaac Newton, PRS (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is regarded by many as the most influential scientist in history. ... Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the... Albert Einstein photographed by Oren J. Turner in 1947. ... This article is in need of attention from an expert on the subject. ... Wikiquote has a collection of quotations related to: Space Attempting to understand the nature of space has always been a prime occupation for philosophers and scientists. ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ... The Planck time is the natural unit of time, denoted by tP. It is considered the smallest possible measurement of time. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left). ... The deepest visible-light image of the cosmos. ... According to the Big Bang theory, the Universe originated in an extremely dense and hot state (bottom). ...

Contents


Regularities in Nature

In order to measure time, one must record the number of times a phenomenon which is periodic had occured. The regular recurrences of the seasons, the motions of the sun, moon and stars were noted and tabulated for millennia, before the laws of physics were formulated. The sun was the arbiter of the flow of time, but time was known only to the hour, for millennia. In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable. ... This article is about divisions of a year. ... In physics, motion means a change in the position of a body with respect to time, as measured by a particular observer in a particular frame of reference. ... The Sun is the star at the center of our Solar system. ... Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ... The Pleiades star cluster A star is a massive body of plasma in outer space that is currently producing or has produced energy through nuclear fusion. ... A physical law or a law of nature is a scientific generalization based on empirical observations. ... A watch Attempting to understand time has long been a prime occupation for philosophers, scientists and artists. ... The hour (symbol: h) is a unit of time. ... A millennium is a period of time, literally equal to one thousand years (from Latin mille, thousand, and annum, year). ...

I farm the land from which I take my food.
I watch the sun rise and sun set.
Kings can ask no more.

-- as quoted by Joseph Needham Science and Civilisation in China Joseph Terence Montgomery Needham (December 9, 1900 – March 24, 1995) was a British biochemist and pre-eminent authority on the history of Chinese science. ...


In particular, the astronomical observatories maintained for religious purposes became accurate enough to ascertain the regular motions of the stars, and even some of the planets.


Measuring Time

At first, timekeeping was done by hand, by priests, and then for commerce, with watchmen to note time, as part of their duties. The tabulation of the equinoxes, the sandglass, and the water clock became more and more accurate, and finally reliable. For ships at sea, boys were used to turn the sandglasses, and to call the hours. Hourglass An hourglass, also known as a sandglass or sand timer, is a device for the measurement of time. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... Hourglass An hourglass, also known as a sandglass or sand timer, is a device for the measurement of time. ...


The use of the pendulum, ratchets and gears allowed the towns of Europe to create mechanisms to display the time on their respective town clocks; by the time of the scientific revolution, the clocks became miniaturized enough for families to share a personal clock, or perhaps a pocket watch. At first, only kings could afford them. Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ... A ratchet can be: the Cwn Annwn in Brythonic mythology, the hounds of Annwn a mechanical device for controlling rotational motion a musical instrument; see ratchet (instrument) a Transformer; see Ratchet (Transformer) a character, from the Ratchet & Clank series a ficitional character, Nurse Ratched, from One Flew Over the Cuckoo... Spur gears found on a piece of farm equipment. ... Europe is conventionally considered one of the seven continents which, in this case, is more a cultural and political distinction than a physiogeographic one. ...


Galileo Galilei discovered that a pendulum's harmonic motion has a constant period, which he learned by timing the motion of a swaying lamp in harmonic motion at mass, with his pulse. Galileo Galilei Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was an Italian astrologer, physicist, astronomer, and philosopher who is closely associated with the scientific revolution. ... A harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement : where is a positive constant. ... Joseph Cardinal Ratzinger (now Pope Benedict XVI) presiding at the 2005 Easter Vigil Mass in place of Pope John Paul II. Mass is the term used of the celebration of the Eucharist in the Latin rites of the Roman Catholic Church and the Anglican Church. ... In medicine, a persons pulse is the throbbing of their arteries as an effect of the heart beat. ...


Mechanical pendulums clocks were widely used in the 18th and 19th century, and have largely been replaced by quartz and digital clocks in general use and atomic clocks, which can theoretically keep accurate time for millions of years, in scientific use. A pendulum clock uses a pendulum as its time base. ... A clock (from the Latin cloca, bell) is an instrument for measuring time. ... An atomic clock is a type of clock that uses an atomic resonance frequency standard as its counter. ...


The current smallest measurable times are on the order of 10 − 15 seconds. It is theorized that there is a smallest possible time, called the Planck time, which is on the order of 10 − 44 seconds. Look up Second in Wiktionary, the free dictionary The second (symbol: s) is the SI base unit of time. ... The Planck time is the natural unit of time, denoted by tP. It is considered the smallest possible measurement of time. ...


Galilean Time

In his Two New Sciences, Galileo used a water clock to measure the time taken for a bronze ball to roll a known distance down an inclined plane; this clock was The Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638) was Galileos final book and a sort of scientific testament covering much of his work in physics over the preceding thirty years. ... Galileo Galilei Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was an Italian astrologer, physicist, astronomer, and philosopher who is closely associated with the scientific revolution. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... This article deals with the physical structure. ...

"a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.".1

Galileo's experimental setup to measure the literal flow of time (see above), in order to describe the motion of a ball, preceded Isaac Newton's statement in his Principia: Sir Isaac Newton, PRS (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is regarded by many as the most influential scientist in history. ... Newtons own copy of his Principia, with hand written corrections for the second edition. ...

I do not define time, space, place and motion, as being well known to all.2

The Galilean transformations assume that time is the same for all reference frames. A watch Attempting to understand time has long been a prime occupation for philosophers, scientists and artists. ... Wikiquote has a collection of quotations related to: Space Attempting to understand the nature of space has always been a prime occupation for philosophers and scientists. ... Place is a term that has a variety of meanings in a dictionary sense, but which is principally used as a noun to denote location, though in a sense of a location identified with that which is located there. ... In physics, motion means a change in the position of a body with respect to time, as measured by a particular observer in a particular frame of reference. ... The Galilean transformation is used to transform between the coordinates of two coordinate systems in a constant relative motion in Newtonian physics. ... Frame of reference - Wikipedia, the free encyclopedia /**/ @import /skins-1. ...


Newtonian physics and linear time

See classical physics Classical physics is physics based on principles developed before the rise of quantum theory, including the special theory of relativity. ...


In or around 1665, when Isaac Newton derived the motion of objects falling under gravity, the first clear formulation for mathematical physics of a treatment of time began: linear time, conceived as a universal clock. Events March 4 - Start of the Second Anglo-Dutch War. ... Sir Isaac Newton, PRS (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is regarded by many as the most influential scientist in history. ... It has been suggested that gravitation be merged into this article or section. ... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ...

Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.3

The water clock mechanism described by Galileo was engineered to provide laminar flow of the water during the experiments, thus providing a constant flow of water for the durations of the experiments, and embodying what Newton called duration. A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... Laminar flow (bottom of pic) and turbulent flow (top of pic) over a submarine hull. ...


Lagrange (1736-1813) would aid in the formulation of a simpler version of Newton's equations. He started with an energy term, L, named the Lagrangian in his honor: Lagrange may mean: Joseph Louis Lagrange, mathematician and mathematical physicist A Lagrange point in physics and astronomy The Lagrange_Multiplier mathematical technique Places in the United States: Lagrange, Georgia Lagrange, Indiana Lagrange, Maine Lagrange, New York (three places): Lagrange, Dutchess County Lagrange, Orange County Lagrange, Wyoming County Lagrange, Ohio Lagrange, Virginia...

frac{d}{dt} frac{partial L}{partial dot{theta}} - frac{partial L}{partial theta} = 0.

The dotted quantities, {dot{theta}} denote a function which corresponds to a Newtonian fluxion, whereas θ denote a function which corresponds to a Newtonian fluent. But linear time is the parameter for the relationship between the {dot{theta}} and the θ of the physical system under consideration. Some decades later, it was found that, under a Legendre transformation, Lagrange's equations can be transformed to Hamilton's equations; the Hamiltonian formulation for the equations of motion of some conjugate variables p,q (for example, momentum p and position q) is: Fluxion was Isaac Newtons term for the derivative of a fluent, or continuous function (see: Calculus). ... Fluent was the term used by Isaac Newton to denote a continuous function. ... In mathematics, two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: f and g are then said to be related by a Legendre transformation. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ...

dot p = -frac{partial H}{partial q} = {p,H} = -{H,p}
dot q =~~frac{partial H}{partial p} = {q,H} = -{H,q}

in the Poisson bracket notation. Thus by transformation to suitable functions, the solutions to sets of these first order differential equations can be more easily implemented or visualized than the second order equation of Lagrange or Newton, and clearly show the dependence of the time variation of conjugate variables p,q on an energy expression. In mathematics and classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition of the time-evolution of a dynamical system in the Hamiltonian formulation. ...


This relationship, it was to be found, also has corresponding forms in quantum mechanics as well as in the classical mechanics shown above. Fig. ... In physics, classical mechanics or Newtonian mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies. ...


Thermodynamics and the paradox of irreversibility

1824 - Sadi Carnot scientifically analyzed the steam engines with his Carnot cycle, an abstract engine. Along with the conservation of energy, which was enunciated in the nineteenth century, the second law of thermodynamics noted a measure of disorder, or entropy. 1824 was a leap year starting on Thursday (see link for calendar). ... Sadi Carnot Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French mathematician who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics. ... A steam engine is a heat engine that makes use of the thermal energy that exists in steam, converting it to mechanical work. ... A heat engine is an engine that uses heat to produce mechanical work by carrying a working substance through a cyclic process. ... Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature, pressure, and volume changes on physical systems at the macroscopic scale. ... Disorder may refer to : A disease, in medicine Randomness (lack of order), in information theory This is a disambiguation page — a list of pages that otherwise might share the same title. ... For other senses of the term, see entropy (disambiguation). ...

See the arrow of time for the relationship between irreversible processes and the laws of thermodynamics. In particular, Stephen Hawking identifies three arrows of time5: Conservation of energy is possibly the most important, and certainly the most practically useful of several conservation laws in physics. ... For other senses of the term, see entropy (disambiguation). ... Physical processes at the microscopic level are either entirely or mostly (see below) time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level this is not the case: there is an obvious... Stephen Hawking in 2005 Professor Stephen William Hawking, D.Phil. ...

  • Psychological arrow of time - our perception of an inexorable flow.
  • Thermodynamic arrow of time - distinguished by the growth of entropy.
  • Cosmological arrow of time - distinguished by the expansion of the universe.

For other senses of the term, see entropy (disambiguation). ...

Electromagnetism and the speed of light

In 1864, James Clerk Maxwell presented a combined theory of electricity and magnetism. He combined all the laws then known relating to those two phenomenon into four equations. These vector calculus equations which use the del operator (nabla) are known as Maxwell's equations for electromagnetism. In free space, the equations take the form: 1864 was a leap year starting on Friday (see link for calendar). ... James Clerk Maxwell (June 13, 1831–November 5, 1879) was a Scottish mathematical physicist, born in Edinburgh. ... Electricity is a property of matter that results from the presence of electric charge. ... In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. ... Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ... In vector calculus, del is a vector differential operator represented by the nabla symbol, ∇. In the three-dimensional Cartesian coordinate system R3 with coordinates (x, y, z), del can be defined as or alternatively, where is the standard basis in R3. ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess a property known as electric charge, and is in turn affected by the presence and motion of such particles. ...

nabla times mathbf{E} = - frac{1}{c} frac{partial mathbf{B}}{partial t}
nabla times mathbf{B} = frac{1}{c} frac{partial mathbf{E}}{partial t}
nabla cdot mathbf{E} = 0
nabla cdot mathbf{B} = 0

where

c is a constant that represents the speed of light in vacuum
E is the electric field
B is the magnetic field.

The solution to these equations is a wave, which always propagates at speed c, regardless of the speed of the electric charge that generated it. The wave is an oscillating electromagnetic field, often embodied as a photon which can be emitted by the acceleration of an electric charge. The frequency of the oscillation is variously a photon with a color, or a radio wave, or perhaps an x-ray or cosmic ray. The fact that light was predicted to always travel at speed c gave rise to the idea of the luminiferous aether and the detection of the absolute reference frame. The failure of the Michelson Morley experiment to detect any motion of the Earth relative to light helped bring about relativity and the downfall of the idea of absolute time. In free space, Maxwell's equations have a symmetry which was exploited by Einstein in the twentieth century. Cherenkov effect in a swimming pool nuclear reactor. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Radiation resistance is that part of an antennas feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna. ... The luminiferous aether: it was hypothesised that the Earth moves through a medium of aether that carries light In the late 19th century the luminiferous aether (light-bearing aether), or ether, was a substance postulated to be the medium for the propagation of light. ... The Michelson-Morley experiment, one of the most important and famous experiments in the history of physics, was performed in 1887 at what is now Case Western Reserve University, and is considered to be the first strong evidence against the theory of a luminiferous aether. ...


Einsteinian physics and time

See special relativity 1905, general relativity 1915. A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. SR theory is based on the previous works of... 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... 1915 (MCMXV) was a common year starting on Friday (see link for calendar). ...


Einstein's 1905 special relativity challenged the notion of an absolute definition for times, and could only formulate a definition of synchronization for clocks that mark a linear flow of time4: Albert Einstein photographed by Oren J. Turner in 1947. ... 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. SR theory is based on the previous works of...

If at the point A of space there is a clock ... If there is at the point B of space there is another clock in all respects resembling the one at A ... it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. ... We assume that ...
1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B, and also with the clock at C, the clocks at B and C also synchronize with each other.

In 1875, Hendrik Lorentz discovered the Lorentz transformation, upon which Einstein's theory of relativity, published in 1915, is based. The Lorentz transformation states that the speed of light is constant in all inertial frames, frames with a constant velocity. Velocity is defined by space and time: 1875 was a common year starting on Friday (see link for calendar). ... Painting of Hendrik Lorentz by Arnhemensis Hendrik Antoon Lorentz (July 18, 1853, Arnhem – February 4, 1928, Haarlem) was a Dutch physicist and the winner of the 1902 Nobel Prize in Physics for his work on electromagnetic radiation. ... The Lorentz transformations (LT), were discovered and published by Joseph Larmor in 1897. ... Albert Einstein photographed by Oren J. Turner in 1947. ... This article is in need of attention from an expert on the subject. ... Cherenkov effect in a swimming pool nuclear reactor. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... This article is about velocity in physics. ...

textbf{V}={dover t}

where

d is distance
t is time

From this one can show that if the speed of light is not changing between reference frames, space and time must be so that the moving observer will measure the same speed of light as the stationary one. Time in a moving reference frame is shown to run more slowly than in a stationary one by the following relation:

textbf{T}={{t}oversqrt{1 - v^2/c^2}}

where

T is the time in the moving reference frame
t is the time in the stationary reference frame
v is the velocity of the moving reference frame relative to the stationary one.
c is the speed of light

Moving objects therefore experience a slower passage of time. This is known as time dilation. Cherenkov effect in a swimming pool nuclear reactor. ... This article is in need of attention from an expert on the subject. ...


One may ask which reference frame is really the moving one, since observers in both would "feel" as if they were standing still and assume the other frame is the one in motion. This gives rise to such paradoxes as the Twin paradox. For other meanings of Paradox, see Paradox (disambiguation). ... The twin paradox, sometimes called the clock paradox, stems from Paul Langevins 1911 thought experiment in special relativity: one of two twin brothers, undertakes a long space journey with a high-speed rocket at almost the speed of light, while the other twin remains on Earth. ...


That paradox can be resolved using Einstein's General theory of relativity, which uses Riemannian geometry, geometry in accelerated, noninertial reference frames. Employing the metric tensor which describes Minkowski space: General relativity (GR) or general relativity theory (GRT) is the theory of gravitation published by Albert Einstein in 1915. ... In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ... In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ...

left[(dx^1)^2+(dx^2)^2+(dx^3)^2-c(dt)^2)right],

Einstein developed a geometric solution to Lorentz's transformation that preserves Maxwell's equations. His field equations give an exact relationship between the measurements of space and time in a given region of spacetime and the energy density of that region. Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... For other topics related to Einstein see Einstein (disambig) Introduction In physics, the Einstein field equation or Einstein equation is a tensor equation in the Einsteins theory of general relativity. ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ...


Einstein's equations predict that time should be altered by the presence of gravitational fields by the following relation: It has been suggested that gravitation be merged into this article or section. ...

T=frac{dt}{sqrt{left( 1 - frac{2GM}{rc^2} right ) dt^2 - frac{1}{c^2}left ( 1 - frac{2GM}{rc^2} right )^{-1} dr^2 - frac{r^2}{c^2} dtheta^2 - frac{r^2}{c^2} sin^2 theta ; dphi^2}}

Where:

T is the gravitational time dilation of an object at a distance of r.
dt is the change in coordinate time, or the interval of coordinate time.
G is the gravitational constant
M is the mass generating the field
sqrt{left( 1 - frac{2GM}{rc^2} right ) dt^2 - frac{1}{c^2}left ( 1 - frac{2GM}{rc^2} right )^{-1} dr^2 - frac{r^2}{c^2} dtheta^2 - frac{r^2}{c^2} sin^2 theta ; dphi^2} is the change in proper time dτ, or the interval of proper time.

Or one could use the following simpler approximation: Gravitational time dilation is a phenomenon of the time running at the vicinity of a mass slower than at infinite distance from that mass (in space without any other masses). ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... Proper time is time as measured by the clock for an observer who is traveling through spacetime. ... Proper time is time as measured by the clock for an observer who is traveling through spacetime. ...

frac{dt}{dtau} = frac{1}{ sqrt{1 - left( frac{2GM}{rc^2} right)}}

Time runs slower the stronger the gravitational field, and hence acceleration, is. The predictions of time dilation are confirmed by particle acceleration experiments and cosmic ray evidence, where moving particles decay slower than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon of gravitational redshift and delays in signal travel time near massive objects such as the sun. The Global Positioning System must also adjust signals to account for this effect. Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the gradient of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity. ... A 1960s single stage 2MeV linear Van de Graaff accelerator, here opened for maintenance A particle accelerator is a device which uses electric and/or magnetic fields to propel electrically charged particles to high speeds. ... Cosmic rays can loosely be defined as energetic particles originating outside of the Earth. ... This article is in need of attention from an expert on the subject. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ...


Einstein's theory was motivated by the assumption that every point in the universe can be treated as a 'center', and that correspondingly, physics must act the same in all reference frames. His simple and elegant theory shows that time is relative to the inertial frame, i.e. that there is no 'universal clock'. Each inertial frame has its own local geometry, and therefore it's own measurements of space and time. This geometry is related to the energy of the reference frame. In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...


Einstein's theory gave us our modern notion of the expanding universe that started in the big bang. Using relativity and quantum theory we have been able to roughly reconstruct the history of the universe. In our epoch, during which electromagnetic waves can propagate without being disturbed by conductors or charges, we can see the stars, at great distances from us, in the night sky. (Before this epoch, there was a time, 300,000 years after the big bang, during which starlight would not have been visible.) The age of the Universe is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch back to the Big Bang. ... According to the Big Bang theory, the Universe originated in an extremely dense and hot state (bottom). ...


Quantum physics and time

See quantum mechanics Fig. ...


There is a time parameter in the equations of quantum mechanics. The Schrödinger equation 6 Fig. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...

H(t) left| psi (t) rightrangle = i hbar {partialoverpartial t} left| psi (t) rightrangle

can be transformed by the Wick rotation, into the diffusion equation (Schrodinger himself noted this). The meaning of this transformation is not understood, and highly controversial. In physics, a Wick rotation is the process by which a theory in Euclidean space is analytically continued into one in Minkowski space and vice versa. ... The heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. ...


It is also theorized that time obeys an uncertainty relation in quantum physics with energy: In quantum physics, the Heisenberg uncertainty principle states that one cannot assign with full precision values for certain pairs of observable variables, including the position and momentum, of a single particle at the same time even in theory. ...

Delta E Delta T ge frac{hbar}{2}
where
ΔE is the uncertainty in energy
ΔT is the uncertainty in time
hbar is Planck's constant

The more precisely one measures the duration of an event the less precisely one can measure the energy of the event and vice versa. This equation is different from the standard uncertainty principle because time is not an operator in quantum mechanics. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... In Wikipedia, precision has the following meanings: In engineering, science, industry and statistics, precision characterises the degree of mutual agreement among a series of individual measurements, values, or results - see accuracy and precision. ... An event is something that takes place; an occurrence and arbitrary point in time. ... In mathematics, an operator is some kind of function; if it comes with a specified type of operand as function domain, it is no more than another way of talking of functions of a given type. ...


Dynamical systems

See dynamical systems and chaos theory, dissipative structures In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... A dissipative system (or dissipative structure) is an open system which is operating far from thermodynamic equilibrium within an environment that exchanges energy, matter or entropy. ...


One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consquence of chaos (i.e. nonlinearity/irreversibility): the characteristic time, or rate of information entropy production, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise. Parameterizations are used in a General circulation model (GCM) to represent processes that are not directly simulated, either because the corresponding equations are not included or because the processes are too small for the model resolution. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... This article belongs in one or more categories. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Irreversibility is that property of an event which makes reverting back to the state before the occurrence of the event impossible. ... The characteristic time of a system is the time it takes for the system to undergo a specific change. ... Entropy of a Bernoulli trial as a function of success probability. ... A system is an assemblage of inter-related elements comprising a unified whole. ... Mandelbrot set, popularized by Benoît Mandelbrot Mandelbrot, (ger; almond-bread ), may refer to: Benoît Mandelbrot, a French mathematician largely responsible for later interest in fractal geometry Mandelbrot set, a fractal popularized by Benoît Mandelbrot This is a disambiguation page — a navigational aid which lists other pages that might otherwise share... 1/f noise is a signal or process with a frequency spectrum such that the spectral energy density is proportional to the reciprocal of the frequency. ...


See also

Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... Physical processes at the microscopic level are either entirely or mostly (see below) time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level this is not the case: there is an obvious...

Further reading

Ilya Prigogine (January 25, 1917 – May 28, 2003) was a Belgian physicist and chemist noted for his work on dissipative structures, complex systems, and irreversibility. ... Beno t Mandelbrot was the first to use a computer to plot the Mandelbrot set. ... Michel Serres (born September 1, 1930) is a French philosopher and author with an unusual career. ... Thomas Samuel Kuhn (July 18, 1922 – June 17, 1996) was an American intellectual who wrote extensively on the history of science and developed several important notions in the philosophy of science. ...

Notes


  Results from FactBites:
 
Time - Wikipedia, the free encyclopedia (2013 words)
Time is also a matter of significant social importance, having economic value ("time is money") as well as personal value due to an awareness of the limited time in each day and in our lives.
Time is currently one of the few fundamental quantities (quantities which cannot be defined via other quantities because there is nothing more fundamental known at present).
However, some aspects of time use are relatively stable over long periods of time, such as the amount of time spent traveling to work, which despite major changes in transport, has been observed to be about 20-30 minutes one-way for a large number of cities over a long period of time.
Time [Internet Encyclopedia of Philosophy] (15898 words)
If physical time, psychological time, and biological time are three different kinds of time, then three answers are required to the question "What is time?" and some commentary is required regarding their relationships, such as whether one is the most fundamental.
Spacetime is four-dimensional and a continuum, with time being a distinguished, one-dimensional sub-space of this continuum.
Proper time along a worldline in 4-d spacetime is the time elapsed by an object having that worldline, as shown on an ideal clock having the same worldline.
  More results at FactBites »

 

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